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# Power Triangle and Power Factor in AC Circuits

## Power in AC circuit

### Active Power (P)

The product of voltage (RMS) and current (RMS) with the cosine of the angle between them, in an AC circuit is termed as *active power*. It is measured in *watts (W)*. For a *pure inductive* and *pure capacitive* circuit, the active power being *zero*.

**Active Power,**

P = VI cos φ

### Reactive Power (Q)

The product of voltage (RMS) and current (RMS) with sine of the angle between them, in an AC circuit is known as *reactive power*. It is measured in *VAR (Volt-Ampere Reactive)*.

**Reactive Power,**

Q = VI sin φ

### Apparent Power (S)

The product of voltage (RMS) and current (RMS) is called as the apparent power. It is measured in *VA (Volt-Ampere)*.

**Apparent Power**

S = VI

## Power Triangle

The *power triangle* is the geometrical representation of the apparent power (S), active power (P) and reactive power (Q) in an AC circuit.

### Case 1 – Inductive Circuit

In an *inductive circuit*, the current *lags behind* the voltage. Therefore, the reactive power lags behind the active power i.e. an inductor absorbs lagging reactive power and delivers leading reactive power. Hence, the power triangle for a Inductive circuit,

### Case 2 – Capacitive Circuit

In a *capacitive circuit*, the circuit current leads the voltage across the capacitor. Therefore, the reactive power leads ahead of active power i.e. a capacitor absorbs leading reactive power whereas delivers lagging reactive power. Hence, the power triangle for a capacitive circuit,

## Power Factor in AC circuit

The *power factor* of an AC circuit can be defined as the ratio of the active power to the apparent power (total power), i.e.,

$$\mathrm{Power\:Factor=\frac{Active\:Power}{Apparent\:Power}}$$

$$\mathrm{\Rightarrow\:PF=\frac{VI\:\cos\varphi}{VI}=\cos\varphi}$$

Hence, the power factor of an AC circuit is the cosine of phase angle between the voltage and current. It should be noted that, the phase angle (Φ) is the angle between the phase voltage and phase current, not between the line voltage and line current.

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